Completely continuous and weakly completely continuous abstract segal algebras

Abstract

Let A be a Banach algebra. It is obtained a necessary and sufficient condition for the complete continuity and also weak complete continuity of symmetric abstract Segal algebras with respect to A, under the condition of the existence of an approximate identity for B, bounded in A. In addition, a necessary condition for the weak complete continuity of A is given. Moreover, the applications of these results about some group algebras on locally compact groups are obtained. © Indian Academy of Sciences.